Goal

Concurrent manipulation and design optimization are possible in
augmented coordinates [dnelson99][dnelson98] at kilohertz rates.
This ability to visualize kinematic reach and collision workspace
during the optimization of a mechanical design objective is the next
step in mouse and haptics interaction with CAD models.
See also advanced work on solid finger tracing and assembly
surface constraints Fast
Surface Gradients for Solving Time-Varying Contact Constraints,
Haptics Tracing, and Collision Dynamics (write dnelson@cs.utah.edu
for the password).
By using augmented coordinates, we establish joint constraints at a
local scope; that is, joints are defined as constraints rather than
with joint angles or other reduced coordinates. Problems with
kinematic loops, such as in Stewart platforms, 4 bar mechanisms,
largely go away. Also, the ability to write surface contact and
nonholonomic
constraints is also possible in augmented coordinates. The
analysis of a mechanism's closed loop inverse dynamics can be done in
linear time using this formulation[dnelson99], a superior approach to
an earlier method [nahvi,dnelson98].

Finger Surface Tracing

The haptic interaction with assemblies also requires tracing
mechanical surfaces with point contact [tthompso,dnelson97], or in a more
recent development, with a parametric surface model for the finger.
Previous efforts with point-to-surface tracing have used offset
surfaces to give a finger a spherical volume. Surface tracing with a
solid finger model is a more natural, intuitive approach that the
previous work in point tracing. Both methods are local algorithms in
that global minimal distance computations are required. The local
property allows them to run at an update rate in excess of 10kHz.

Virtual proxies are important in the penetrating case.
The maximal distance is required by the haptics tracing algorithm.
Global discontinuities such as "chopping though" an object are not
desirable. Because a haptics device such as a PHANToM can hold a user
to within .3mm of the surface, local discontinuities should not occur
except for regions of very high curvature. Since the velocity formulation is the "most local", it
is the distance computation of choice for tracing surface updates for
the penetrating case.

Optimization and Graph Theory

The manipulation performance of large models is also a concern in this
work.
We use a linear time (given certain mild assumptions) optimization
algorithm to perform the "self-assembly" or interactive
reassembly/inverse kinematics tasks required for concurrent
optimization and manipulation. Our optimization method is organized
around graph-theoretic results from the mechanical engineering community.

Support

Support for this research was provided by NSF Grant MIP-9420352, by
DARPA grant F33615-96-C-5621, and by the NSF and DARPA Science and
Technology Center for Computer Graphics and Scientific Visualization
(ASC-89-20219).